It is definitely a good idea to study the impact of extreme cases and/or "outliers" when conducting CFA because they can have an influence on the size of the covariances/correlations based on which factor models are estimated. I would remove extreme cases/outliers only if you are certain that they represent invalid scores. In your case, the impact at least on the factor loading(s) and fit statistics seems to be modest.
Dear madam, Always remove outliers from the data set whether it is a CFA, EFA or any other statistical test. otherwise it will inflate the data even in CFA.
For CFA, It will have an impact on correlation and standardised regression weights, this will make your model invalid whenever you are going to check model validity. However, if you have a normally distributed data then outlier should not be presented in your data.
Dear David Eugene Booth , I checked the mean, trimmed mean, skewness and kurtosis values, along with histogram, and Normal Q-Q plots, and they indicate that the data is normally distributed. However, I also have a few outliers. Does having a few outliers mean that my data is not normally distributed? I am confused.
It depends on the outliers but always remember that normally distributed means normally distributed and if there are outliers your distribution at best is a contaminated normal. So how much contamination is really important? Investigate that if you can but please remember that there are robust methods to help you. See the attachment for more details. Best wishes David Booth